Question

Let $f\left(x\right)=\sin \frac{\pi }{x}$ and $D=\{x:f(x)>0\}$, then $D$ contains

• A. $(\frac{1}{3},\frac{1}{2})$
• B. $(\frac{1}{5},\frac{1}{4})$
• C. $(-1,-\frac{1}{2})$
• D. $(-\pi ,-\frac{1}{2})$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $(\frac{1}{3},\frac{1}{2})$
B $(\frac{1}{5},\frac{1}{4})$
C $(-1,-\frac{1}{2})$

$f\left(x\right)=\sin \frac{\pi }{x}$ in this we have to find $x$

For which $f\left(x\right)>0$

$\sin \frac{\pi }{x}>0$

$2n\pi <\frac{\pi }{x}<(2n+1)\pi nϵI$

$2n<\frac{1}{x}<2n+1nϵI$

$\frac{1}{2n+1}<x<\frac{1}{2n}nϵI$

for $n=1,2,-1$; option $A,B,C$ matches respectively.